Добавил:
Sekretar
kiopkiopkiop18@yandex.ru
t.me/Prokururor I Вовсе не секретарь, но почту проверяю
Опубликованный материал нарушает ваши авторские права? Сообщите нам.
Вуз:
Предмет:
Файл:Ординатура / Хирургия / Библиотека им академика М.И. Перельмана / Книга_3787_Библиотеки_им_академика_М_И_Перельмана
.pdf
Appendix 4: Coronary Flow Regulation 425
https://t.me/med1917
Table 6.4 (A) Order distribution of passive vessel parameters obtained by fitting Eq. (6.77) to the
experimental data of pressure versus diameter
(A) Passive vessel parameters
Order R
0 2.65 3.13 3.20 2.43 0 19.28 In situ
1 3.89 4.44 4.51 3.59 0 17.24 In situ
5 22.73 33.12 35.02 10.9 0.61 20.11 In vitro
6 32.43 49.37 51.38 16.41 1.88 14.23 In vitro
6 57.54 81.03 85.53 32.17 1.64 21.24 In vitro
7 91.50 125.97 133.52 51.6 0.96 23.54 In vitro
0 416.48 820.41 829.6 401.52 30.39 3.35 In vitro
(μm) R80(μm) Ap(μm) Bp(μm) ϕp(mmHg) Cp(mmHg) Data source
0
a
a
b
b
b
b
c
(B) Myogenic vessel parameters
Order R
(μm) ρm(μm) ϕm(mmHg) Cm(mmHg) Data source
80
1 3.20 2.24 30.00 33.00 Extrapolated
1 4.44 3.29 40.00 35.00 Extrapolated
5 33.12 26.47 69.40 57.20 In vitro
6 49.37 50.96 (48.74) 125.4 (102.98) 87.3 (66.89) In vitro
6 81.04 77.86 (74.54) 148.9 (102.98) 135.4 (87.78) In vitro
7 125.97 74.14 77.3 51.31 In vitro
b
b
b
b
10 730.50 0 0 20.00 Extrapolated
(C) Shear vessel parameters
Order R
(μm) F
80
τmax
Kτ(dynes/cm2) Data source
1 3.20 0.00 15.00 Extrapolated
1 4.44 0.00 15.00 Extrapolated
5 33.12 0.43 1.04 (15.60) In vitro
6 49.37 0.83 1.33 (19.95) In vitro
6 81.04 1.00 0.45 (6.75) In vitro
7 125.97 0.62 0.78 (11.70) In vitro
b
b
b
b
10 730.5 0.00 20.00 Extrapolated
The vessel load free passive radius for each order, R
radius, R
, under 80 mmHg (Kassab, Imoto, et al., 1993) based on Eq. (6.77). (B) Order distribu-
80
at 0 mmHg, is calculated from the vessel cast
0
tion of the myogenic regulation parameters. For orders 5–7, the values (bold-faced numbers) are
obtained from a fit of Eq. (6.95) to data on isolated vessels (Liao & Kuo, 1997). For the purpose of
interpolating to vessels of orders 8 and 9, the active properties for vessels of order 10 are set to zero
assuming they show no myogenic response. Data for in-between orders are extrapolated or
interpolated from the measured ones. (C) Order distribution of the flow regulation parameters. In
vitro data (bold-face) is taken from a study on single vessels of orders 5–7 (Liao & Kuo, 1997).
Following Liao and Kuo (Liao & Kuo, 1997), the figures in brackets for K
are adjusted to account
τ
for the presence of hemoglobin in vivo by increasing them approximately 10 times to achieve
physiological levels of flow perfusion. Parameters for vessel orders 1 and 10 are extrapolated
assuming they have no flow response. Reproduced from Namani et al. (2018) by permission
a
References for in situ (Kassab et al., 1999)
b
Reference for in vitro isolated microvessels (Liao & Kuo, 1997)
c
Reference for in vitro data (Hamza et al., 2003)
426 6 Network Analysis of Coronary Circulation: II. Pulsatile Flow
https://t.me/med1917
Under ex vivo conditions, the compliant isolated vessels collapse. In vivo, the
vessel tethering to the surrounding myocardium supports it from collapse (see Chap.
3). To comply with these observations, the level of B
integrated into the model. The isolated vessel passive parameters (A
is set to zero, and tethering is
p
, ϕp, and Cp) are
p
re-estimated from the ex vivo experimental data on isolated vessels (Liao & Kuo,
1997) for vessel orders 5–7 under the constraint of B
¼ 0. Parameters for vessel
p
orders 0–1 are obtained by curve fitting Eq. (6.77) to in situ diameter–pressure data
and parameters of order 10 are extracted from a sigmoidal fit of ex vivo data (Chap. 3).
The passive parameters as a function of vessel radius across all orders are
obtained by fitting a quadratic curve through all data points of the parameter, A
and linear fits to ϕ
and Cp(Table 6.4A). The vessel radius is transformed to the
p
radius under 80 mmHg pressure to be compatible with the in situ data (Kassab,
Imoto, et al., 1993). Given a vessel radius, the fits are used to interpolate the passive
material properties between orders 1 and 8 (Fig. 6.19).
Active Vessel Properties The active wall properties are determined by VSMCs
which are affected predominantly by myogenic (pressure), flow (shear), and metabolic control mechanisms. Literature data on the vascular response to these mechanisms are primarily on the steady-state response (Liao & Kuo, 1997). There is
paucity of data on the dynamics of coronary control and much of the transient
response relates to changes in heart rate including the combined effects of multiple
flow regulation mechanisms (Dankelman, Vergroesen, Han, & Spaan, 1992). The
analysis of flow regulation, however, requires detailed knowledge of the dynamics
of each flow control mechanism which is currently unavailable. In the absence of
such data, the steady-state responses including the functional role of each control
mechanism and of their interactions are considered whereas the mechanics of the
vascular system and its interaction with the myocardium are dynamically analyzed
under these quasi-steady state control conditions.
The radius of the active vessel varies dynamically under a cyclical trans-vascular
pressure. The vessel response is determined by the active dynamic vessel wall
stiffness. In vitro studies of isolated vessels (Halpern et al., 1978) have shown that
the vessel dynamic stiffness is proportional to the active tension, T
. This propor-
act
tionality is in line with findings of in vitro isolated myocytes and myocyte culture
(Campbell, Patel, & Moss, 2003; Lipowsky, Kovalcheck, & Zweifach, 1978; Yadid
& Landesberg, 2010). It is thought that in the heart and skeletal muscle, both the
stiffness and active tension are proportional to the number of attached actin–myosin
cross-bridges. Since the contractile machinery in VSMC is actin–myosin as well, it is
reasonable to adopt the same relationship for the arterial wall, and with the same
proportionality constant. To this end, the total vessel wall tension is taken as the sum
of the passive and active components. Under equilibrium, this wall tension balances
the contributions of the trans-vascular pressure and of the tethering tension. Hence,
the following can be obtained:
,
p
Appendix 4: Coronary Flow Regulation 427
https://t.me/med1917
Fig. 6.19 Distribution of vessel passive parameters Ap, φp, and Cp(Eq. 6.53) over the vessel radii
(Kassab, Imoto, et al., 1993). The minimum vessel radius, B
sources are listed in Table 6.4 for vessel order 1–10. Because the data are incomplete, values for
in-between orders for which data are not available are interpolated based on a linear fit for A
quadratic fits for φ
Reproduced from Namani et al. (2018) by permission
and Cp. The data sources a, b, and c are listed in the footnotes of Table 6.4.
p
, is set to zero for all vessels. The data
p
p
and
ΔP R
reg
The tension of the passive wall, T
T
ΔP; A¼ ΔP
pas
pRreg
¼ R
regcp
where A
, Bp, Cp, and ϕpare passive vessel parameters (Bp¼ 0).
p
ΔP; AþT
, stems from the passive elements given by:
pas
R
reg
tan
ΔP; A
πR
Ap B
teth
reg
¼T
B
þT
act
pas
π
p
þ ϕ
p
2
p
ð6:82Þ
ð6:83Þ
The active tension is assumed to depend solely on the vessel circumference
(or radius) and activation. This is due to the dependence of VSMC active tension
in the vessel wall on the actin/myosin overlap which is directly related to the wall
circumference or radius. Tethering does not affect the active tension–radius relationship. Hence, at a given passive tension, the force balance in Eq. (6.44) under
T
¼ 0 determines the active tension as a function of both the R
teth
reg
and the
activation level A.
The active constitutive relationship allows the determination of the passive
vascular dynamic stiffness, k
, as foll ows:
pas
428 6 Network Analysis of Coronary Circulation: II. Pulsatile Flow
https://t.me/med1917
!
k
pasRreg
dT
pas
2πdR
¼
¼
R
reg
¼
2 Ap B
d ΔP:RðÞ
2πdR
ΔP; Ac
!(
p
p
cptan
þ
R
1
¼
reg
2π
dR
dΔP
1 þ tan
πR
reg
Ap B
ΔP; A
þ ΔP
ΔP
πR
ΔP; A B
reg
Ap B
p
p
:
2
π
2
9
ΔP; A B
p
2π
π
p
2
þ ϕ
>
>
>
=
p
ð6:84Þ
>
>
>
;
when the regulated radius (R
) is less than the passive zero-pressure radius (R0), the
reg
tethering tension becomes effective. The tethering “stiffness” is defined similar to
passive stiffness (from Eq. 6.84) as:
k
tethRreg
¼
d
T
teth
2πdR
reg
C
str
R
¼
R
0
π
reg
ð6:85Þ
where the minus sign designates the decrease in vessel radius to an increase in
tethering stiffness. Since the dynamic stiffness of the active vessel to stretch perturbations is found to be linearly proportional to the active tension (Halpern et al.,
1978), the level is evaluated from their data as:
where C
k
ΔP; A¼ C
act
¼ 30.6 mm-1is the slope of the linear regression and C0¼ 4.85 kPa is the
1
T
1
act
ΔP; Aþ C
0
ð6:86Þ
intercept. The total vascular dynam ic stiffness is the sum of active, passive, and
tethered stiffness components given by:
kΔP; A¼ k
ΔP; Aþ k
act
pasRreg
þ k
tethRreg
ð6:87Þ
Given the above expressions for each stiffness term, the total vascular dynamic
stiffness can be evaluated from Eq. (6.8 8 ).
Similar to Eq. (6.84), the vessel compliance under dynamic loading of ΔP(t)
around ΔP is obtai ned from the vessel wall dynamic stiffness, k, as follows:
dR
dΔP
ΔP, A
R
¼
2πkR
reg
reg
ΔP; A
; A
ΔP
ð6:88Þ
Wall Tension with No Tethering The regulated radius as a function of average
trans-vascular pressure is given by:
Appendix 4: Coronary Flow Regulation 429
https://t.me/med1917
^
R
reg
ΔP¼ R
ΔP AΔR
p
ΔP
m
ð6:89Þ
where the passive contribution of the av erage trans-vascular pressure derived as:
"#()
ΔP
pas
^
R
¼ ϕ
reg
þ cptan
p
π
^
R
reg
Ap B
B
π
p
2
p
ð6:90Þ
The wall tension due to passive elements of the vessel wall as a function of the
regulated radius is:
^
R
reg
¼ ΔP
T
pas
pas
^
R
reg
:^R
reg
ð6:91Þ
The wall tension due to active elements is the difference between the total wall
tension and the wall tension due to passive elements of the vessel wall and is given
by:
T
act
A;^R
reg
¼ ΔP^R
reg
ΔP
pas
¼^R
ΔP ΔP
reg
^
R
reg
pas
ð6:92Þ
The wall tension contribution from the passive and active elements in the vessel
wall are calculated with the above equations for experimental data of Liao and Kuo
(1997). Since data are available at only some pressure values, sigmoidal models of
pressure–diameter relationships of different order vessels are used to calculate the
wall tensions.
For the case of active tension for a vessel with tethering, the constitutive equation
is modified to include addit ional pressure on wall due to tethering as given by:
ΔP
totalRreg
; A
¼ ΔPR
reg
; A
þ
T
tethRreg
R
ð6:93Þ
reg
The regulated radius, R
ΔP; Ais an unknown variable and is determined by
reg
the iterative solution of the force balance equation as:
ΔP R
ΔP; Aþ T
reg
tethRreg
¼ T
actRreg
þ T
pasRreg
; A
ð6:94Þ
Myogenic Regulation The myogenic regulation results from VSMC contraction in
response to local wall stress as determined by the trans-vascular pressure. The
myogenic diameter reduction is expressed by a sigmoidal function of the timeaveraged trans-vascular pressure ΔP (Young et al., 2012) as:
430 6 Network Analysis of Coronary Circulation: II. Pulsatile Flow
https://t.me/med1917
!"#
ΔR
ΔP¼
m
ρ
π
m
π
arctan
2
ΔP ϕ
C
2m
m
m
ð6:95Þ
where ρ
under which the myogenic radius change is highest, C
is the myogenic response amplitude, ϕmis the trans-vascular pressure
m
is the myogenic response
m
bandwidth, and m is a shape factor. The parameters for Eq. (6.95) for the various
vessel orders are given in Table 6.4.
The regulated vessel radius under quasi-static loading is taken to be a function of
the total activation level, A, and of the mean trans-vascular pressure, ΔP (Liao &
Kuo, 1997). The maximum myogenic reduction in radius ΔR
(A ¼ 1), R
, is attenuated with the total activation (A < 1) (Liao & Kuo, 1997)to
reg
under full activation
m
yield the regulated radius as:
R
¼ R
reg
ΔP; A¼ R
reg
ΔP AΔR
p
ΔP
m
ð6:96Þ
where the total activation (A) due to myogenic, shear stress and metabolites is given
by:
A ¼ 1 F
Expressions for F
and F
τ
ðÞ1 F
are listed below. The product form of Eq. (6.97)
meta
ðÞ ð6:97Þ
τ
meta
between the metabolic and flow regulations relates the respective residual activities
(1 F
)and (1 F
τ
). This form is mathematically identical to the physiologically
meta
based additive model proposed and experimentally validated by (Liao & Kuo, 1997).
The longitudinal distribution of myogenic parameters of vessel orders 5–7is
obtained by fitting Eq. (6.95) to ex vivo data under varying pressures (Liao & Kuo,
1997). Since capillaries (order 0) and large epicardial arteries (order 10) do not
exhibit myogenic radius changes , the myogenic amplitude (ρ
) of these vessels is
m
taken as zero. The interpolated sigmoidal parameters of other order vessels are listed
in Table 6.4B (Fig. 6.20). Due to the lack of experimental data for the myogenic
amplitude, ρ
, for vessel orders 1–5, the myogenic sensitivity curve is extrapolated
m
from order 5 down to order 1 vessels assuming a constant shape factor m ¼ 2, the
level estimated from the in vitro data (Young et al., 2012). The myogenic sensitivity,
ρ
/R, is assumed to be the same for all order 1 vessels.
m
From Eq. (6.95), ϕ
corresponds to ΔPof highest ΔRm, the comparison of the
m
ex vivo parameter estimates with the data of order 6 vessels showed that the
myogenic diameter reduction ΔR
from the estimates of ϕ
ΔP at highest ΔR
around ϕ
(Eq. 6.95), the estimates of Cmare adjusted to maintain this symmetry.
m
. Hence, ϕmfor order 6 vessels is adjus ted to the value of
m
. Furthermore, since the (ΔR
m
reaches peak levels at a ΔP which is different
m
ΔP) relationship is symmetric
m
These adjustments have an insignificant effect on the fit of Eq. (6.95) to the data. The
passive and fully myogenic active (A ¼ 1) vascular pressure–diameter relationship
Appendix 4: Coronary Flow Regulation 431
https://t.me/med1917
Fig. 6.20 Distribution of the vessel myogenic parameters ρm, φm, and Cm(Eq. 6.95) over their
cast radii, R
Reproduced from Namani et al. (2018) by permission
80 mmHg
(Kassab, Imoto, et al., 1993). The data sources are listed in Table 6.4.
(PDR) are calculated from Eqs. (6.77) and (6.95). PDR distribution across the
various vessel orders is presented in Fig. 6.21.
Flow (Shear) Regulation The shear regulation induces relaxation of the myogenic
contracted vascular wall which is mediated by nitric oxide (NO) production by the
endothelial cells in response to local wall shear stress. The shear fractional deactivation is taken to be dependent on the average shear stress,
τjjand is expressed by
(Liao & Kuo, 1997):
τ
where K
F
¼ F
τ
τmax
is the wall shear stress constant and F
τ
jj
K
þ τ
jj
τ
is the maxi mum deactivation due
τmax
ð6:98Þ
to wall shear stress. The parameters for Eq. (6.98) of various vessel orders are
summarized in Table 6.4C (Fig. 6.22).
Liao and Kuo (Liao & Kuo, 1997) pointed out that the values of their in vitro
measured K
are too low due to the presence of hemoglobin which binds to NO and
τ
hence decreases the in vivo sensitivity to shear. In their flow analysis in an idealized
symmetric network without MVI, they increased K
by a factor of 150 which
τ
allowed the vessels to respond to shear stress under physiological conditions. In
the present network simulations, it is found that a factor of 15 is sufficient
(Table 6.4C).
Metabolic Regulation Early studies on the vasomotor response in the microcirculation observed that dilation spreads over a much larger area than can be explained
by diffusion (Krogh, Harrop, & Rehberg, 1922). More recent studies established the
predominant role of the endothelium layer in conducting vasodilatory stimulus
(Emerson & Segal, 2000; Furchgott & Zawadzki, 1980; Looft-Wilson, Payne, &
Segal, 2004) via cell-to-cell coupling (Larson, Kam, & Sheridan, 1983).
432 6 Network Analysis of Coronary Circulation: II. Pulsatile Flow
https://t.me/med1917
Fig. 6.21 Pressure–diameter relationship under passive and active vessel conditions. The model
predicted vessel diameter, D, normalized by the vessel diameter under zero pressure, D
passive state (solid line) and under full myogenic state (dashed line), and the diameter reduction
under full metabolic activation (dotted line), as functions of the trans-vascular pressure ΔP, for (a)
small arteriole of order 5, (b) intermediate arteriole (I.A.) of order 6, (c) large arteriole (L.A.) of
order 6, and (d) small artery of order 7. Corresponding data are the symbols (open circle, open
square, and open triangle, respectively) from in vitro studies of isolated vessels (Liao & Kuo, 1997)
as shown in Figure. Reproduced from Namani et al. (2018) by permission
Fig. 6.22 Distribution of the vessel shear parameters F
(Kassab, Imoto, et al., 1993). The data sources are listed in Table 6.4. Reproduced from Namani
R
80
et al. (2018) by permission
and Kτ (Eq. 6.57) over their cast radii,
τmax
, in the
0
To establish the specific pathway by which coronary vessel diameter is regulated
has been difficult due to redundancies in control pathways, difference between
species, conflicting results in different studies, different (at times opposite) effects
at rest versus during exercise (see review in (Duncker & Bache, 2008)), and at times
opposite effects on vessels of different sizes (Gorman & Feigl, 2012). In humans,
there are additional uncertainties due to inadequate control of the coronary
Appendix 4: Coronary Flow Regulation 433
https://t.me/med1917
endothelial state (Duncker & Bache, 2008). Notwithstanding these difficulties, it is
established that coronary local metabolic control is not primarily due to adenosine,
ATP-dependent K
+
channels, NO, prostaglandins, and inhibition of endothelin
(reviews in (Duncker & Bache, 2008; Tune, Gorman, & Feigl, 2004)). A number
of mechanisms for the initiation and conduction of vasodilation have been proposed
(Budel, Bartlett, & Segal, 2003; Doyle & Duling, 1997; Figueroa et al., 2007;
Hoepfl, Rodenwaldt, Pohl, & De Wit, 2002; Looft-Wilson et al., 2004; Murrant &
Sarelius, 2002; Rivers, 1997; Tallini et al., 2007; Xia & Duling, 1995). A specific
pathway that has gained attention proposes that red blood cells (RBCs) may act as
sensors of oxygen and thereby of the metabolic supply/demand imbalance (Ellsworth, 2000). Adenosine triphosphate (ATP) is found to be released from RBCs in
response to hypoxia and hypercapnia (Bergfeld & Forrester, 1992; Ellsworth,
Forrester, Ellis, & Dietrich, 1995). These conditions occur in the capillaries and
venules under high metabolic demand when oxygen supply is lower than demand
(Collins, McCullough, & Ellsworth, 1998; Farias III, Gorman, Savage, & Feigl,
2005; Gorman & Feigl, 2012). Venules are thus optimally positioned to monitor the
metabolic state of the tissue (Jackson, 1987; Segal, 2005).
Based on a number of studies, the adenine nucleotides regulation mechanism is
proposed (Farias et al., 20 05; Gorman & Feigl, 2012; Gorman, Ogimoto, Savage,
Jacobson, & Feigl, 2003; Gorman et al., 2010), where ATP released by RBCs in the
venules under high metabolic demand is broken down to its metabolites, adenosine
diphosphate (ADP) and adenosine monophosphate (AMP). All three adenine nucleotides are potent coronary vasodilators (Gorman et al., 2003). They bind to P1
(AMP) and P2 (ATP and ADP) purinergic receptors on the endothelial cells
(Burnstock, 2007; Gorman et al., 2003) thereby stimulating endothelial synthesis
of NO which interacts with the smooth muscle cells (SMCs) in the vessel walls to
dilate the vessels thus reducing their resistance to flow (Sprague, Ellsworth, Stephenson, & Lonigro, 1996).
The vasodilatory signal is believed to be conducted (conducted response, CR)
across the capillaries (Collins et al., 1998; Tigno, Ley, Pries, & Gaehtgens, 1989)to
the endothelial cells of upstream arterial microvessels, likely via endothelial cells
gap junctions (Collins et al., 1998; Domeie r & Segal, 2007; Figueroa et al., 2007;
Segal & Duling, 1987; Segal & Duling, 1989). The vasodilatory effect of CR is
believed to decay exponentially with distance into the upstream arterioles (Delashaw
& Duling, 1991; Hirst & Neild, 1978; Xia & Duling, 1995). Additional experimental
support for the conducted response is found in studies in which ATP application
inside small arterioles, outside capillaries, and inside venules, produced retrograde
conducted vasodilatory response (Collins et al., 1998; Duza & Sarelius, 2003;
McCullough, Collins, & Ellsworth, 1997).
In addition to the sustained and decaying CR, (Figueroa & Duling, 2008) found
that short stimulation of Acetylcholine (ACh) evoked transient vasodilation that
spread along the entire vessel length (up to 2 mm) without decay. This study
(Namani et al., 2018) focuses on the steady-state effect of sustained metabolic
demand. Since the characteristics of that non-decaying signal and its functional
434 6 Network Analysis of Coronary Circulation: II. Pulsatile Flow
https://t.me/med1917
consequences for the entire network flow under sustained metabolic demand remain
unclear, this mechanism is not included in the model.
Importantly, the CR is not restricted to the vasodilatory mechanism due to
adenine nucleotides but is rather a generic framework which represents a range of
possible vasodilatory signaling, spreading from the capillaries to upstream arter ioles
Extravascular synthesized metabolites such as muscle released ATP, adenosine, NO,
and potassium which may diffuse radially into the arteriolar walls and relax the
SMCs, however, are not considered. A theoretical analysis by Lo et al. (2003)
showed that local responses alone provide insufficient flow regulation. Countercurrent exchange by diffusion of vasoactive arachidonic acid metabolites between
paired venules and arterioles (Hammer, Ligon, & Hester, 2001) is not included
since pairing and close alignment tend to be typical of larger and intermediate sized
venules and arterioles. The major portion of resistance to flow, and therefore of flow
regulation, resides in the smaller sized arterioles. These smaller vessels are highly
affected by the CR signal due to their proximity to the venules.
The CR model (Arciero, Carlso n, & Secomb, 2008) integrates the signaling
effects along the various network pathways, from the pre-capillary arterioles to
each specific upstream vessel. Hence, the metabolic activation F
i
in an upstream
meta
vessel i is expressed by:
where u
i
u
X
i
F
meta
i
is the number of terminal vessels fed by the upstream vessel i, S
F
¼
j¼1
i
mterm
u
i
S
j
, j
; S
i
i
j
i
L
j
L
0
¼ e
; i ¼ 1 ...n ð6:99Þ
i
is the
j
strength of the response in an ith vessel conducted from its jth terminal vessel and L
is the decay characteristic length. The metabolic signal in the jth terminal order
1 vessel F
i
is a direct function of the local oxygen supply/demand imbalance.
, j
mterm
The conducted response is found to decay exponentially with the path length, L
towards the upstream vessels (Arciero et al., 2008; Delashaw & Duling, 1991;
Goldman et al., 2012; Xia & Duling, 1995) with a characteristic length,L
, which
0
determines the rate of decay of the metabolic activation with path length (Eq. 6.99).
The total metabolic activation, F
all jth terminal vessels fed by that vessel. A reference value of L
i
,inanith vessel is taken to be the average from
meta
¼ 1 mm is selected
0
for the decay characteristic length. This value lies within the measured range of
different vascular beds (0.15–2.5 mm, (Hald et al., 2012)).
The metabolic signal in each j terminal order 1 vessels, F
i
, depends on the
, j
mterm
local demand/supply imbalance. In control theory, the control signal is the system
desired output which in the coronary circulation is the requisite terminal arterioles
perfusion which balances the metabolic O
demand. This is irrespective of the
2
metabolites or mechanisms involved. Hence, although the terminal arterioles flow
is not physiologically a sensed signal, its requisite level represents the metabolic
demand regardless of the involved metabolite pathways. Our choice of a metabolic
signal is supported by the findings that coronary flow correlates well with an increase
0
i
,
j
Соседние файлы в папке Библиотека им академика М.И. Перельмана